Well, without leading zeroes, and ignoring negatives, the 4 digit base 7 numbers are 1000 base 7 (aka, 343) through 6666 base 7 (aka, 2400).

The first of these divisible by 11 is 352, and the last is 2398.  So the total number divisible by 11 is (2398-352)/11 + 1 = 187 numbers

Or maybe we are looking for the number divisible by 11 base 7 (aka, 8).  The first one divisible by 8 is 344, and the last is 2400.  So the total number divisible by 8 is (2400-344)/8 + 1 = 258 numbers